Is it technically correct to say that Anti-HBeAg is detectable during acute HBV? The graph in FA (pg 166 FA14) and also Pathoma show Anti-HBeAg levels beginning at around the 5th month post-exposure and peaking during the window period.

Yes, Anti-HBeAg can occur during the acute phase, window phase, and the chronic phase.

That's why we only use it to define early recovery ('window period') when only Anti-HBe, and Anti-HBc (Igm) occur, in the absence of antigen.
But, you would know this is a recovery phase anyway, simply from the lack of antigen.